On Kadison’s Carpenters theorem

MARTIN ARGERAMI; PEDRO G. MASSEY

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY

Amer. Math. Soc.

Año: 2009 vol. 137 p. 3679 - 3687

0002-9939

  Let M be a II_1 factor with trace t( ), A in  M a masa and E_A the  unique trace preserving conditional expectation onto A. Under some technical                assumptions on the inclusion of A in M, which hold true for any semiregular masa of a    separable factor, we show that for elements a in certain dense families of the positive part of the unit ball of A, it is possible to find a projection p in M such that E_A(p) = a. This shows a new family of instances of a conjecture by Kadison, the so-called “carpenter's theorem”.